Preserve UVs when modifying topology
In the following animation I'm double-tapping the g key to move points and edges.



In the video, an entire corner piece was moved and I don't think this can be easily done using Blender yet.  There may be an Addon for this, I'm not sure.

As mentioned in the comments above, the UV Project Modifier can be useful and there is also a way to do something similar in Cycles.

It's called Box Mapping and uses the Texture Coordinates node to create coordinates using various methods, in this case I used the Object Coordinates.  This way, you can edit the mesh all you like without affecting the texture and then once you have the model ready, you can bake the box mapped texture to the UV coordinates.

Here is a quick Cycles render that shows Blended Box Mapping in Action.  



This is just a plain cube with no UV coordinates.  There are 3 other cubes that are being used as Boolean Objects on the cube that is being rendered.  The next image shows the node and model setup for the brick box looking thing



You can pretty much do whatever you want to this model and not have to worry about the UV Coordinates.



Finally, the Booleans are applied, the model is unwrapped and the texture is baked.  





Now back to the original question.  Loop Cut and Slide Ctrl+r can be set to maintain UV's.  The Inset tool does this as welli.